Alternative approach to second-order linear differential equations with constant coefficients

Abstract

In this paper, we give a straightforward method to solve non-homogeneous second-order linear differential equations with constant coefficients. The advantage of this method is that it does not require the uniqueness and existence theorem of the solution of the problem of initial values. Neither does it require the characterization of the linear independence of solutions by the Wronskian, nor the unnatural method of variation of parameters. As an additional benefit of this method, we obtain a single formula for the general solution, that is, a formula that expresses the general solution independent of the nature of the roots of the characteristic equation, namely it does not matter if the roots are equal or different real numbers or if they are two conjugated complex numbers.

Keywords:

• linear differential equations
• method of variation of parameters
• general solution

Acknowledgements

The authors would like to thank the reviewers for their valuable comments and suggestions to improve the quality of this article.